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Mathematics
Mathematics
Problem
Evaluate the limit
lim
n
→
∞
∑
i
=
1
n
sin
(
π
(
2
i
−
1
)
2
n
)
π
n
.
\lim_{n\to\infty}\sum_{i=1}^{n}\sin\left(\frac{\pi(2i-1)}{2n}\right)\,\frac{\pi}{n}.
n
→
∞
lim
i
=
1
∑
n
sin
(
2
n
π
(
2
i
−
1
)
)
n
π
.
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